Question

Tʜᴇ ᴛᴡᴏ sɪᴅᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢᴜʟᴀʀ ғʟᴀɢ ᴀʀᴇ 30 ᴄᴍ ᴀɴᴅ 40 ᴄᴍ. Fɪɴᴅ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴛʜɪʀᴅ sɪᴅᴇ ɪғ ᴛʜᴇ ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ғʟᴀɢ ɪs 130 ᴄᴍ ?

Answer 1

Given: The two sides of a triangular flag are 30 cm and 40 cm. & the perimeter of triangular flag is 130 cm.

Need to find: The third side?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

❍ Let's Consider the third side of triangular flag be x cm.

As we know that,

❝Perimeter of the triangle is Given by Sum of its all three sides i.e ( P ) = a + b + c.❞

Therefore:

$\qquad\star\:\underline{\boxed{\pmb{\sf{Perimeter_{\;(triangle)} = a + b + c}}}}$

where,

• a, b and c are the three sides of the triangle.
• & the Perimeter is Given that is 130 cm

⠀⠀

⠀⠀⠀$\underline{\bf{\dag} \:\mathfrak{Substituting\;the\:values\: :}}$⠀⠀⠀⠀

$:\implies\sf Perimeter_{\;(triangle)} = a + b + c \\\\\\:\implies\sf 30 + 40 + x=130\\\\\\:\implies\sf 130 = 70 + x=130\\\\\\:\implies\sf x = 130 - 70\\\\\\:\implies\underline{\boxed{\pmb{\frak{\purple{x = 60}}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence, the third side of the triangular flag is \textbf{60 cm}.}}}$

Answer 2

Answer:

Given :-

• The two sides of a triangular flag are 30 cm and 40 cm.
• The perimeter of the flag is 130 cm.

To Find :-

• What is the length of the third side of a triangular flag.

Formula Used :-

$\clubsuit$ Perimeter Of Triangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Perimeter_{(Triangle)} =\: Sum\: Of\: All\: Sides}}}$

Solution :-

Let,

$\mapsto \bf Third\: Side_{(Triangular\: Flag)} =\: y\: cm$

Given :

• First Side (a) = 30 cm
• Second Side (b) = 40 cm
• Third Side (c) = y cm

According to the question by using the formula we get,

$\footnotesize\bigstar\: \: \sf\bold{\purple{Perimeter_{(Triangular\: Flag)} =\: Sum\: Of\: All\: Sides}}$

$\longrightarrow \bf Perimeter_{(Triangular\: Flag)} =\: a + b + c$

By putting a = 30 cm, b = 40 cm and c = y cm we get,

And,

• Perimeter = 130 cm

$\longrightarrow \sf 130 =\: 30 + 40 + y$

$\longrightarrow \sf 130 =\: 70 + y$

$\longrightarrow \sf 130 - 70 =\: y$

$\longrightarrow \sf 60 =\: y$

$\longrightarrow \sf\bold{\red{y =\: 60\: cm}}$

Hence, the third side of a triangular flag is :

$\leadsto \sf Third\: Side_{(Triangular\: Flag)} =\: y\: cm$

$\leadsto \sf\bold{\red{Third\: Side_{(Triangular\: Flag)} =\: 60\: cm}}$

${\small{\bold{\underline{\therefore\: The\: length\: of\: third\: side\: of\: a\: triangular\: flag\: is\: 60\: cm\: .}}}}$

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★ VERIFICATION ★

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\blue{Perimeter_{(Triangle)} =\: Sum\: Of\: All\: Sides}}}$

Given :

• Perimeter = 130 cm

$\implies \sf 130 =\: 30 + 40 + y$

By putting y = 60 cm we get,

$\implies \sf 130 =\: 30 + 40 + 60$

$\implies \sf 130 =\: 70 + 60$

$\implies \bf 130 =\: 130$

Hence, Verified.